Frank was appointed as Tottenham boss earlier this month after guiding Brentford to a 10th-place finish in the Premier League last season.
Andrews, a former Irish international, had joined Brentford's backroom staff in 2024 to work as their set-piece expert.
“Keith is a very good fit,” said director of football Phil Giles.
“He gets on with everyone, he’s very open and he’s a learner. Keith is clear in what he wants, he’s detailed, and the players and staff like and respect him.
“He understands the players in the building and the way we’ve played and trained under Thomas Frank.
“Keith will bring his own evolution but isn’t starting from scratch, so hopefully we can make some quick progress."
The 44-year-old has previously held assistant coaching roles with Sheffield United, MK Dons and Ireland.
Frank led Brentford back to the top-flight in 2021 after an absence of 74 years and has established the west London club in the Premier League.
The club's first league game of the new season is at Nottingham Forest on August 17th.